This disclosure provides a method of designing and manufacturing an optical lens which focuses equally over a large range of colors.
The current state of the art requires two lens elements for this purpose.
This disclosure describes a way to succeed with one lens. This achromatic gradient index singlet lens has the potential of reducing the lens count in multi-element imaging systems by up to a factor of two.
The material property that allows a lens to bend light is the refractive index. The higher the refractive index contrast between two materials, the more light will bend at a curved interface between them. A near-universal property of the refractive index for optical materials is that its value changes as a function of the color, or wavelength, of light.
Constant-index materials are achieved only in manmade, highly artificial materials such as photonic bandgap structures—materials probably unsuited for imaging optics in the foreseeable future.
The variation of refractive index as a function of wavelength is referred to as optical dispersion. A highly-dispersive material is one whose index of refraction changes greatly as a function of wavelength.
Because of material dispersion, lenses do not focus light of different colors equally. This presents a problem for imaging. Imaging an object onto film or a camera sensor requires the optical system to bring all colors into focus together. The typical way to do this is to use lenses made of different materials, with different dispersive properties.
An achromatic doublet is the simplest example of how one can focus light of different colors to the same point. This optic consists of two lenses cemented together. One lens is strongly focusing, fabricated from a glass with weak dispersion. The second lens is a negative lens, which means that it weakens the focusing from the first lens, but is designed so that the overall two-lens system still focuses light. One aspect is that the negative lens is made from a highly dispersive material. The amount of wavelength-dependent focusing depends both on the strength of the lens and the dispersiveness of the material. So, by balancing a strongly-focused lens with weak dispersion by a weak, negative lens (which bends the colors the other way) with strong dispersion, one can have balanced chromatic performance in a lens that is still a positive, focusing lens.